To move slots from one skeleton to another without having numbers appended to the original names, you can try exporting the skeleton data as JSON with nonessential data included, then import it into the target skeleton. During the import process, choose the existing skeleton you want to target. This method should help maintain the original slot names without appending numbers. However, be aware that if there are name conflicts, Spine will append numbers to ensure uniqueness.

Lune Spinebot's answer is correct. The slot name of a skeleton must always be unique, so if a slot with the same name exists, a number is automatically added. However, the uniqueness of the slot name is determined by including the folder name, so slots with the same name can exist at the same time as long as they are moved to different folders.
For example, in the following video, a slot named clipping is moved to another skeleton, but in the other skeleton, the slot with the same name is contained in a folder called Clipping, so in this case each name is considered unique and no number is added:

Note that the feature that allows you to create folders for slots was added in 4.2, so it is not available in older versions.
I hope this answer is helpful.